{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction into System Dynamics using Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "System dynamics is a method devoted to the study of systems, and is thus a tool within the Systems Thinking tool kit. It uses simple graphical notations to model systems such as stock and flow diagrams. These diagrams contain specific components and symbols to describe systems. This tutorial gives an introduction to the elemens of stock and flow diagram using the BPTK-Py framework."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The tutorial explains system dynamics with a population model. The model shows how the population changes overtime and which factors influence the population value.\n",
    "\n",
    "![Image](./images/population.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Now, let's create the model. It is used to store all stocks, converters and flows. The model runs for 10 years (starttime = 0, stoptime = 10) and we want to analyse the results after each year (dt = 1). In the next steps we are going to add the stocks and flows to the model.\n",
    "\n",
    "We want to simulate how the population changes in the next ten years under external influences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from BPTK_Py import Model\n",
    "from BPTK_Py import sd_functions as sd\n",
    "\n",
    "model = Model(starttime=1.0,stoptime=10.0,dt=1.0,name='Population')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stocks\n",
    "\n",
    "A stock represents a part of a system whose value at any given instant in time depends on the systems past behavior. The value of the stocks at a particular instant in time cannot simply be determined by measuring the value of the other parts of the system at that instant in time – the only way you can calculate it is by measuring how it changes at every instant and adding up all these changes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Image](./images/stock_population.png)\n",
    "\n",
    "The stock in our model represents the population at each timestep. Initially, we assume 80 mio. people living in our fictional country.  We create a model by entering `model.stock(<name>)`. The name of our stock is \"population\".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "population = model.stock(\"population\")\n",
    "population.initial_value = 80000000.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "population.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The population does not change. There are no other factors influencing the number of people. To simulate changes in the population, we need births and deaths. We add these factors by using flows."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Flows\n",
    "\n",
    "Flows represent the rate at which the stock is changing at any given timestep. They either flow into a stock (causing it to increase) or flow out of a stock (causing it to decrease)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Image](./images/flow_births.png) ![Image](./images/flow_deaths.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us make this model simple and just suppose 1,000,000 babies are born and 2,000,000 people die each year. The flows are defined by using the method `model.flow(<name>)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "births = model.flow(\"births\")\n",
    "deaths = model.flow(\"deaths\")\n",
    "births.equation = 1000000.0\n",
    "deaths.equation = 2000000.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "births.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "deaths.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Equations\n",
    "\n",
    "To connect elements we require equations. These are mathematical operations that are evaluated at each timestep. We combine the flows with our stock by setting the ``equation`` field of ``population``."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Image](./images/stock_flow_population.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In our simple example, the population is the sum of births minus the deaths plus the initial value or the value from the last timestep.\n",
    "\n",
    "The Logic in System Dynamics is always the same: Values at timestep ``t`` depend on the result at ``t-1`` Let us look at the population:\n",
    "```\n",
    "\n",
    "population.equation = births - deaths\n",
    "\n",
    "population (1)  = 80,000,0000 (start time)\n",
    "population (2) = population(1) + (births(2) - deaths(2)) = 80,000,000 + (1,000,000 - 2,000,000) = 79,000,000\n",
    "population (3) = population(2) + (births(2) - deaths(2)) = 79,000,000 + (1,000,000 - 2,000,000) = 78,000,000\n",
    "\n",
    "and so on...\n",
    "```\n",
    "\n",
    "See how easy it is to define this behavior:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "population.equation = births - deaths"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And let's check whether we are able to obtain the expected results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "population(1): 80000000.0\n",
      "population(2): 79000000.0\n",
      "population(3): 78000000.0\n"
     ]
    }
   ],
   "source": [
    "print(\"population(1): \" + str(population(1)))\n",
    "print(\"population(2): \" + str(population(2)))\n",
    "print(\"population(3): \" + str(population(3)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "population.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In reality, the number of births or deaths is not fixed, we usually work with ratios. They change depending on the population and external factors (diseases, medical supply, food supply etc.). In system dynamics, we model such behavior with converters. \n",
    "\n",
    "### Converters\n",
    "\n",
    "Converters either represent parts at the boundary of the system (i.e. parts whose value is not determined by the behaviour of the system itself) or they represent parts of a system whose value can be derived from other parts of the system at any time through some computational procedure.\n",
    "\n",
    "Let us model the following model in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Image](./images/population.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the image above, the converters are represented by circles. In Python, we define converters with ``model.converter`` or ``model.constant``. ``constants`` are converters with a constant value (i.e. they never change).\n",
    "\n",
    "We want to model the birth rate and death rate that are influenced by the food supply."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "birthRate = model.converter(\"birthRate\")\n",
    "deathRate = model.converter(\"deathRate\")\n",
    "foodAvailablePerPerson = model.converter(\"foodAvailablePerPerson\")\n",
    "foodAvailable = model.constant(\"foodAvailable\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Connectors \n",
    "\n",
    "Much like in causal loop diagrams the connectors of a system show how the parts of a system influence each other.  Stocks can only be influenced by flows (i.e. there can be no connector that connects into a stock), flows can be influenced by stocks, other flows, and by converters. Converters either are not influenced at all (i.e. they are at the systems boundary) or are influenced by stocks, flows and other converters.\n",
    "\n",
    "Please note that we do not explicitly model connectors but create the connection by defining equations. Equations are expressive enough to represent interactions between model elements.\n",
    "\n",
    "Since `foodAvailable` is a constant, we can initiliaze it with a float value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "foodAvailable.equation = 80000000.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The converters `foodAvailablePerPerson` and `birthRate` are formulas. `foodAvailablePerPerson` depends on `population` and `foodAvailable`. The more people the less food per person. The birth rate decreases if we have less than one unit food per person."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "foodAvailablePerPerson.equation = foodAvailable / population\n",
    "\n",
    "birthRate.equation = 0.01 * foodAvailablePerPerson\n",
    "\n",
    "births.equation = birthRate * population"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define the death rate in our model using a non-linear relationship (depending on food available per person). We capture this relationship in a lookup table (often also called \"graphical function\" in the System Dynamics context) that we store in the `points` property of the model (using a Python list)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.points[\"deathRate\"] = [\n",
    "    [0.0,1.0],\n",
    "    [0.1,0.670320046036],\n",
    "    [0.2,0.449328964117],\n",
    "    [0.3,0.301194211912],\n",
    "    [0.4,0.201896517995],\n",
    "    [0.5,0.135335283237],\n",
    "    [0.6,0.0907179532894],\n",
    "    [0.7,0.0608100626252],\n",
    "    [0.8,0.0407622039784],\n",
    "    [0.9,0.0273237224473],\n",
    "    [1.0,0.0183156388887]\n",
    "]\n",
    "\n",
    "deaths.equation = deathRate * population"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can easily plot the lookup table to see whether it has the right shape:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot_lookup(\"deathRate\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we have defined all components. Let us plot them. We first register the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "import BPTK_Py\n",
    "bptk = BPTK_Py.bptk()\n",
    "bptk.register_model(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bptk.plot_scenarios(\n",
    "    scenarios=\"base\",\n",
    "    scenario_managers=\"smPopulation\",\n",
    "    equations=[\"population\",\"deaths\",\"births\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scenarios\n",
    "\n",
    "BPTK Py creates a scenario `base` by default when registering the model. However, it is boring just to examine one scenario. We want to make various assumptions to understand the behavior of the model or the system. Changing values can lead to different outcomes. For this purpose, the BPTK Py framework provides a powerful scenario management enabling us to create different scenarios.\n",
    "\n",
    "We set up a scenario manager using a Python dictionary. The scenario manager identifies the baseline constants of the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "scenario_manager = {\n",
    "    \"smPopulation\":{\n",
    "        \"model\": model,\n",
    "        \"base_constants\": {\n",
    "        \"population\": 80000000.0,\n",
    "        \"foodAvailable\": 80000000.0\n",
    "        },\n",
    "        \"base_points\":{\n",
    "          \"deathRate\": [\n",
    "            [0.0,1.0],\n",
    "            [0.1,0.670320046036],\n",
    "            [0.2,0.449328964117],\n",
    "            [0.3,0.301194211912],\n",
    "            [0.4,0.201896517995],\n",
    "            [0.5,0.135335283237],\n",
    "            [0.6,0.0907179532894],\n",
    "            [0.7,0.0608100626252],\n",
    "            [0.8,0.0407622039784],\n",
    "            [0.9,0.0273237224473],\n",
    "            [1.0,0.0183156388887]]\n",
    "        }\n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The scenario manager has to be registered as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "bptk.register_scenario_manager(scenario_manager)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After registering the scenario mangager, we can define and register more scenarios. Let us change `foodAvailable` from 80,000,000 units to 700,000 units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "bptk.register_scenarios(\n",
    "    scenarios ={\n",
    "        \"scenario07\": {\n",
    "            \"constants\": {\n",
    "                \"foodAvailable\": 700000.0,\n",
    "            }\n",
    "        }\n",
    "    },\n",
    "    scenario_manager=\"smPopulation\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can plot our scenarios `base` and `scenario07` and see how changing `foodAvailable` affects the population. We plot the `population` for both scenarios."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zh3JyciQ51V8vvvyCrv3n9Zrw8COStTqsRw+9+fbrGjzo+Ji5LrzofL07Y6bGj5ugTZs2qekeTXX6mSN01dVXRirQatSooTfenq4H/z1O016ZpmmvvqaaNWtq7xbNde55o9S5U6e0z+H2O27RjBkzdd+992vTpk06rMehuufeu2K2qfboeZjeeGu67rj9Tv3r3vslSQcedIAef+IxHdL94G2as07dOnp+6nO67pobNPbGm9V0j6a66OILtNtuu+miC8r/vPTs2UOPPf6I7v/XA7r+2jFq2LCBTh1+qg47rLuOH3JSzNhhp5yseV99rTffeEsvTJkqa23ScCzdzw0AAAAAZJqh6XHV0rVrVztv3rykjy9YsCCyTSza3B/L9p3KlOKSYhUHturgVg3k82UpOys300vaoZYtW679Ox+g68dcq6v/cVWml4Od6PnnpuiiCy7RjJlv69DDulfZOVF9LPn5F/25uer8eQ4AAADvWrbiG9WoUUeN67dU74MGKy83P9NL2i7GmK+ttV0TPUbl2C6iV6c2mV5CxJatRdpaUqStxZsyvRQAAAAAAIByEY4BqFRrVq9RcUlxuWMaNGggv3879t/uYOvWrdeWLUXljqlbl95ZAAAAALArIBwDUKlGDD9Tn37yabljvvu/b7T33s130orSd80/rtULFVzx8c13Xt9JqwEAAAAA7Ej0HKtitrXnWFUSva3SCz3HEOvbb76t8Oqb3Q/trhoJropYVSxcuFB//u/Pcsd06dJFderW2TkLgmfQcwwAAABVBT3HAGAbdTmgS6aXsN3at2+v9u3bVzwQAAAAAFDt+TK9AAAAAAAAACBTCMcAAAAAAADgWYRjAAAAAAAA8CzCMQAAAAAAAHgW4RgAAAAAAAA8i3AMAAAAAAAAnkU4BgAAAAAAAM/KyvQCUDn++OPjTC8horikWCWBrapdd99ML6Vau/OOu3X3nfdo7YbCSp33mIGDJUlvz3ijUudFWRecd5E++eRT/fDjt5leyi5p305d1LNnDz3y2MOVNueyZcu1f+cD9PAj4zR8xGmVNi8AAACAqotwbBdSUrJRgcCmTC9DVtmSsjO9jHLt26mLflv+W+R+Xl6e2rRtoxGnn6ZzR4+Sz1e9iyq///4Hvf3WOxpx+nA1a7ZXppeDbbRy5UqNuf5GzZ71noqLi3XgQQfo1ttuVpcDukTGhMOcZFq1bqX/fvvVTlht9fL8c1O0YcMGnX/BeZleCgAAAIAMIxzbhQQCm7R581+ZXoaysusqK7t2ppdRoQ4d2uvyKy+TJK1aVaAXpkzVP6++Viv/XKkbx47J8Oq2zw/f/6C777xHvXodWSYce+31VzK0Ku95aPy/FQqFtum5mzZt0qCjh+ivVat08SUXavfdd9cTE5/UoGOG6L0PZqvdPu0kSQ0a1Ndjjz9S5vkL5i/Qvx94SH/rc9R2ncOuasrzU/XHH3+UCceaN2+mP1etUHZ21Q74AQAAAFQewrFdUP36mdvOWFj4Q8ZeO12NGjfSsFNOjtw/6+wzdfBB3fXYo4/r2uuv2WX/cZyTk5PpJezyNm3apJo1a27X79BTTz6txYt/0htvT9cRRxwuSTrhhON10IEH67Zb79Azzz0tSapZs2bM73HY1Vf9U5J06qnDtnkNXmSMUY0aNTK9DAAAAAA7UfXeO4Zd0qZNm3TTmLHqst9BatxgD7Vs3kZ9evfT69OdHll33nG36tSqr4ULF+rSiy9Xy+Zt1Hyvlrr80itVXFysjRs36vJLr1TrFu20Z5PmOn/0hSoqKqrwdWvWrKmu3bpq06ZNKigokCT9/vsKjR51nlq3aKfGDfZQj0OP0PPPTYl53rJly1WnVn3de8+/NOmpp3XA/l3VuMEeOrxHL73/3gcxY59/borq1KqvZcuWJ5wjfu5477w9Q6ecPFwd9+msRvWbquM+nXXl5X/X2rXrImPuvONuXXTBJZKkgf2PUZ1a9VWnVn19/PEnkpyeY+G+Y2FbtmzRLWNv1b6duqhhvSbat1MX3TL2Vm3dujVm3L6dumjIoOP136//q/59BqpJwz3Vqf2+Gj9uQkVvbxkV/ZzD/vrrL1115dXq3GG/yDmPOnu0/vjjj8iYkpIS/eve+9TtwEPUqH5TtWvdQZddcoXWrF6zzesf99DDGtjvGLVu0U6N6jdVtwMP0bgHx8taGzPumIGDdcD+XTV//gIdN/gE7dW0uc49x6lGuuC8i7Rvpy4x40OhkB584CF1PeBgNarfVO3bdtRVV14d8zOUpOmvTVeHDu0jwZgkNWjYQMcff5xmvjtLmzdvTvrelpSUaNorr2mffdrpwIMOTDoukfDna/78BTp/9IXau1krNdtjb51z1rlatWpVmfEz3nlXfXr3U9NGe6n5Xi116rDhWrRw0TbPmej3M3qO8hQXF+uO2+/SUb36qEXz1mrScE/1POzIMp+rfTt10aeffKpff/k18vkI/5ySfRYXLFioU4cNV/O9Wqppo73Up3c/vTtjZsyYjz/+RHVq1dfUF17UuIceVueO+6txgz3Up3c/ffvtd+WuHQAAAEDmUDmGKufvV1ytV1+ZpnPOPVsdO3TQ+g0b9MMPP2jeV19ryHGl/2gePeoCNW/eTDfceJ0+/+wLPT1psvLz87VgwQLVrFlT191wjb74/AtNfeFF7bFH05S2Sv7661L5/X7Vrl1bhQWF6t9ngFavXqPR541S0z2aavq013XRBZdodeFqXXLZxTHPfX36m1r11yqdc+7ZqpGbq0mTJmvY0FP1xlvTdehh3SvlvXnu2efl9/t07uhRqlevnn744Qc9+8zzmv/jAr07+x1J0qDBx2rlnyv19KTJuvqfV6lNm9aSpH3cbXjxrLU6ffiZmj1rjk4+ZagOPribvvziS91/37/1448L9OLLsSHB77+t0CknD9ewU07WyacM1bRXp+uG68aoQ4f2aW3hS+Xn/Ndff+lvvfvpz//9qTPOHKHO+3ZWQUGBZr07W7/88qv22GMPd/0jNfeDuTr9jOHq1KmTli5dqomPPaGvv/6v5rw/M6YSKNX1Txg/Qf3699Pg4wYrK8uvD96fqzE33KS1a9dqzE03xJzLhvUbdPzgEzXw6AE67rghqpGXvPLo71dcrUlPPa3+A/rrvAtGa9HCRXrqyaf11Vdfa/Z77yonJ0ehUEj/98OPOmnoiWWef+BBB+rpSZO1cMHCpMHX7FlzVFhYqIsuviDln0e80aPOV716dXX9DddqyZJf9OTjT2nRosV6f+7sSPXhKy+/qnPPOU8dO3XU9WOu04YNGzTx0cfVr+9AfTB3jlq1bpX2nNtjw/oNmvTk0zr+xON06mmnqKQkoLffekcXXXCJAiUBnXnWGZKkO++6XbeMvVVr167TrbffLMkJx5P5+aef1b/PAGVlZeuCC89XrVq1NOX5F3TqsOGaNPlJHXf8kJjxjz7ymIq3Fuu880crGAjooQfHa8RpZ+ib7+btshWpAAAAQHVGOIYqZ8aMd3XmyNN11913lDuufft2mvjEY5Kkc0adrV9++UWPTHhUJ58yVI9NfCRyfMmSX/Tcs1PKhGMlJQEVFjhXglxVsEpPPv6Uvv/uex19zEDl5+frjtvu0ooVf+jV116OhCbnjDpbxwwYpNtvu1PDR5ymevXrReZbuGChPv/yU7Vp20aSdNrwU3XgAd104w03afb7sRUm2+qJpyYqPz8/5li3g7vpvHMv0OeffaHuhx6izp07qdvBXfX0pMk66qjeFQZzM9+dpdmz5uiKKy/TTTffKEkade45aty4icY9NF6zZs5Wv/59I+OXLFmiV6a9pD59/yZJGnH6cHXusL+emfxsWuFYKj/nm2+6Vb8t/y1ma6EkXf2PqyIVXK++Mk3vznhXr73+inof1Tsy5ogjj9AJx52kF194KRKKpLP+r7/9Kua9Pnf0KF1y0WV69JGJ+sc1Vys3NzfyWEFBgW6741ZdfMmF5Z7z/PkLNOmpp3XS0BP1xFMTI8f3ab+Prv77P/XM5Gc16txztGb1Gm3dulVNmjQuM0f42P/+92fS13lx6ksyxmjosKHlrqc8devW0Wuvvyq/3y9J6tihgy679Ao9/9wUnXX2SJWUlOj6a8eoZauWmjn7He22226SnHD2iB69dMvNt+npZ55Ka87tVaduHf3fgu9ifjYXXnS+hgw6Xg8+OC7ye3DsoGP0yITHVBIIJNySGu+Wm2/Tpk2b9clnH6lDh/aSpDNHnq6ehx2pa/95nY4ddIyyskr/Ol2zZq0+//JT5eXlSZJzsY/TztD7732g/gP6bfd5AgAAAKhcbKtElVO7dm3Nm/e1fv99RbnjRp41MuZ+t4O7yVqrM888o8zxv/76q8w2tP98+h+1btlOrVu2U/duPfTE409p4NEDNP7hhyRJM9+dqY4dO8QEJtnZ2brw4gu0ZcsWffjhRzHz9e3XJxKMSc4WuJNPPklffTUvEsJtr3BYY63V+vXrVVhQqEO6HyJJ+vbbb7dpzpnvzpIkXXJpbCXcZZdf4j4eG+zt3WLvSLAkSbm5uera7SAtXbosrdet6OccCoX05ptvqfdRvWKCsTBjjCRp2quvqUXLFtpvv/1UWFAY+dp///20e+3d9dFHH2/T+sPvdSAQ0No1a1VYUKieh/fQpk2b9NNPP8eM9fl8OvuckRWe80x3G97Fl14Uc/zMkWeodp3akZ9F0ZYtkqScqJAnst4azrEt7ph4a9eu07szZqrn4T2260qlo887NxJiSdJpI07V7rV317sznDV++823Wrlypc4+56xIMCZJnTt3Up8+f9Oc2XPKXIygojm3l9/vjwRjJSUlWrN6jQoLCnXkkUfolyW/aN269WnPGQwG9d6c99W3X99IMCZJtWrV0jnnnKX//e9PfRe3ZfK04adGgjFJ6tmzhyRp6dKl23BWAAAAAHY0KsdQ5dx2+y06f/SF2rfj/urUuZN69+6lE086Xl0O6BIzbq+4f/jXrl273ONr166NqQTab//9dMutN7kNuPPUpk1r1W9Q2tNo+fLfNPDoAWXWt0/7fSRJy+LClLZt25YZGw7Lli9fHjP3tlq8aLFuuvFmfTj3ozJh37b8wz+8tgYNGsRUwUlOuFe/ftn+aM2aNSszR506dfTjj/PTet2Kfs4FBQVav269OnbsWO48S35eoqW/LlXrlom3jcb3tEp1/bNmztY9d92rb7/9ToFAIOaxdXH9wRo3blSmoi+R5ct/kyS1axf7u5KTk6NWrVpGfqfy3G2gxXE93yRp6xbnWLKm8dOnTdfWrVt1ynY24m/brk3M/ezsbLVo0ULLlzlrTHYukvMZmTVrtgoKCtSoUaOU56wMU55/QePHTdDCBQvLhHPr169X7dq7pzVfQUGBNm3alPQ8JadP2UFdD4ocjw8l69StI8mpKAMAAABQ9RCOocoZPGSQDj2su2a8M1Mfzv1Qzz37vMaPe1hjbrxeV151RWSc35+48DHZ8fhG6nXr1lGv3r0qa9kpCVc7xQsFgxU+d/369Tpm4GDl1sjVtddfo9atWyk/P0/BYEgnHj+0TBCwo6T6/lYk1Z9zRUKhkNq1a6t7/nVXwsfr1KkTcz+V9X/x+Zc65eTTdPDB3XTf/feq6R5NlZOTre++/V433XizQjb2va4RVSVUGerWq6vc3NyEWyf//HOlJKlp0yYJnzv1hReVn58f05+vOjHGJPxdCqbwGZn26mu68PyL1b9/P1108QVq1KiRsrOzNGvmHE14+JGd+BnxJzye7mcEAAAAwM5BOIYqqWHDhjrjzBE648wRKioq0tATT9Fdd95Tpgn+jtS8eTMtXvxTmeOLFy2W5GzPi/bTT2XH/uxuv2vevLmk0qBm3brYyqPly2OrsxL5+KNPtGrVKr01443INq3o14iWLIRLpHnz5npvzvtaXbg6pnqssKBQhYWF2nvv5inPla7yfs4NGjTQ7rvX0vz55VektWrVSvPmfa0jjjxCPl/l7BSfPv115eTkaPqb02IqtJb+un0VTs2bO1Vrixf/pC5d9o8cLykp0a+/LlW3bl0lOds0O+/bSd/895syc3w972vl5uZGqpaiLf11qT7//AudPOykmK2O2+KnxT+rffvSbYQlJSVatmyZunfvXuZconvSSc5nZLfdaqpBgwZpzSlJderUTrhFN5XPyKuvTNPeLfbW1JenxHwGPvrw4zJjU/2MNGjQQDVr1iz/z4Id+BkBAAAAsOPRcwxVSjAYLLM9MC8vT23btlFxcbE2bdqc5JmVb8DAAZr/43x98P4HkWOBQECPPPyoatSooV69jowZP3vWnJigqmBVgV566RV17XpQZEtlq9YtJTlBV7THJz5Z4XrCwU989ctDD44vMzZ85b34EC6RAQP7S5IeHj8hbt5x7uNlt5Zur1R+zj6fT4MGD9IH788t0zdMKq3COeGk41VYWKgJDz+a8HXWrF6T9vp8xidjTEy10pYtWzTxscfTnitaf/e9nhD3Xj8z+VmtXbM28rOQpCFDBmvBgoX6+OPS35WCVQWaPv119e3XJ+HVFadOfUmSdMqpp2zXOiVp4mOPx5z/lOde0Lq169R/gBOEHXDgAWrcuLEmPfm0Nm3aFBk3f/4CzZnznvr261smrKxoTskJOxcvWqy//vorcuyPP/7QO2+9U+GaE31GVheu1nPPTikztmZ+fpntsYn4/X716ev0UFu0cFHk+MaNG/Xkk5PUtGkT7R8VdAIAAACofqgc2wUVFv6Q6SVssw0bNqrjPp117KCj1blzZ9WpW1c/fP+9npn8rPr266M6dWrvtLVcfsWlmvbqNA0/9QyNPm+Umu7RVNNfe0Off/6Fbr3tZtWtVzdmfPsO7XXMwMEaNfps5ebkatKkydq8abNuvnVs6Zj27dW9+yG67ZbbtWbNGjVq1FAz3nlXa9eurXA93bsfovr16+uC0Rdq9HnnKi8/TzPfnaVVqwrKjN1///1kjNED9/1bq1evVm5uro448nA1bNiwzNh+/fuqT9+/6b5/PaAVK/5Q124H6auv5unFF15S/wH91bdfn7Tfu4qk+nO+cewNmvvBXJ143FCdceYIdd63s9asXqPZs+bo+huvU8+ePXTysKF64/U3dcN1Y/TZfz5Tj549lJXl16+/LtWbr7+pa6+/RsNHnJbW+gYeM0ATHn5Exw06QcNOPVkbN2zUC1OmKjdJn69UdezYQWedPVKTnnpa69dvVJ++R2nRwkV66smntX+X/XX6GSMiY88edZaemfysTh9+pi655CLtXnt3PTHxSQUDAd1w43UJ53/pxZfVtGkT9ep9ZMLH07FmzVodP+REHTvoGP3yy696YuKT6tipo0acPlySlJWVpdvvvFXnnnOe+vc9Wqeedoo2bNigiY8+rt1q7aYxN16f9pySdMaZIzR+3MM6fshJOnPk6Vq3bp2eemKS2rRto2+/+a7MnNGOPmag3nzjLQ0beqqOOfZorVpVoMmTJqtJ0yYxYZsk7X/A/po5c5ZuuO5GdTlgf9WsWTNhj0FJGnPj9frg/Q909IBBOve8UapVq5amPP+Cli1dpkmTn4y5UiUAAACA6of/ot+FZGXVVH5+o4oH7mBW2drWzjr5+Xk6d/Q5mjv3I82cOVvFW4u111576sqrrohcPXFnqd+gvt6dPUO3jL1Vz0x+Ths3blSbtm00fsJDMf+YDxty3CA1aNBADz04Xit+X6F2+7TT1JemqEfPw2LGTXzyMV15+d/18LgJysvL04lDT9A5o85S9249yswZrW69unpl2ou6/robde89/1J2do769vubHp04QW1btY8Z26JlC919750aP26CLrnoMgWDQb35zusJwzFjjJ59frLuuetevfzyq3r1lWlq3KSxrvz75frHNVdvwztXsVR/zo0bN9Z7c2frztvv1ttvvaNnJj+nRo0aqkfPw9S6davI+p957mk99ujjmvL8C3pvzvvKycnWXs2a6fgTjtcRRx6R9vp69uyhxx5/RPf/6wFdf+0YNWzYQKcOP1WHHdZdxw85abvO/b4H7lWLFnvrmcnP6b0576levXoaedYZGnPjDcrJyYmM22233fTmO69rzPU3ady4h1W8tVgHHnSgHp04IWZrYtiXX3ylX5b8oksvu6RStpdOfOJRPfjvh3T7bXcqGAho0OBjddc9d8Ss8aShJyo/P1/3/et+3XrzbcrJyVaPnj10081j1Mr9+aQ7Z5u2bfTkpMd12y136Pprx6hVq5a6/c7btGjR4grDsVNPO0WrV6/RE48/qWv+cZ322msvXXzpxdp991q66ILYPz8uuvhC/bT4Jz377HMaP+5hNWveLGk41qZtG82c865uvulWTRg/QcXFJercuZNeePH5mGo/AAAAANWToUFw1dK1a1c7b968pI8vWLBAHTp0KHP8jz/KbjvLlOKSYpUEtqp23X3l82UpOys300vaoZYtW679Ox+g68dcq6v/cVWmlwNslzvvuFt333mPflz4vfbcc88qO+euasnPv+jPzWX7CAIAAAA727IV36hGjTpqXL+leh80WHm5+Zle0nYxxnxtre2a6DEqx3YRe+xxeKaXELFla5G2lhRpa/GmigcDAAAAAABkEOEYgEq1ZvUaFZcUlzumQYMG8vv9O2lFkFL/uQAAAACA1xCOAahUI4afqU8/+bTcMd/93zfae+/mO2lFkFL/uQAAAACA19BzrIrZ1p5jVUn0tkov9BxDrG+/+bbCq292P7S7amznlR+RHn4u1QM9xwAAAFBV0HMMALZRlwO6ZHoJSICfCwAAAAAk5sv0AgAAAAAAAIBMIRyrhtgKCwC7Hv5sBwAAADKDcKyaycnJUVFRUaaXAQCoZFu3FitgSzK9DAAAAMBzCMeqmQYNGuj333/X6tWrVVJSQqUBAFRj1loFAkFtWL9Rf/zxh9ZvWZXpJQEAAACeQ0P+aqZ27drKzc3VqlWrVFhYqEAgkOkllVESKFEgWKxAoFjG55Pfx68ZACRjFdLWYJE2FBcoSOUYAAAAsNORWlRDNWrUULNmzTK9jKQWL5+vn3+fr6W/f62aNRuoYd29M70kAAAAAACAhNhWCQAAAAAAAM8iHNsBjDEdjTHvGWM2G2P+MMbcYozxZ3pdAAAAAAAAiMW2ykpmjKkraY6k+ZKGSGot6T45QeQNGVwaAAAAAAAA4hCOVb7zJeVJOsFau17SbGPM7pLGGmPucY8BAAAAAACgCmBbZeUbKGlmXAg2VU5gdmRmlgQAAAAAAIBEqByrfO0lvR99wFq73Biz2X3szYysKkOCgYC2bN2Y6WUAAAAAAIA02EwvYCciHKt8dSWtTXB8jftYuUKhkIqKiip7TTvV1i1bVVJcokBJSBuKV2nDhlWZXhIAAAAAAEhTtj+okuISJ6cImUwvZ4chHKsCjDGjJY12727Mz89flMn1bC9/lq9Gdg3/7j6f4ferGispDuZn5/g3Z3odgJfxOQQyi88gkHl8DoHMKtkazPNn+dZv2VRSoOpfTLZ3sgcILyrfGkm1Exyv6z5WhrV2oqSJO3JRQLqMMfOKiwJdM70OwMv4HAKZxWcQyDw+h0BmGWPmFW/Z9T+DNOSvfAvl9BaLMMY0k5TvPgYAAAAAAIAqgnCs8s2Q1N8YUyvq2DBJRZI+zMySAAAAAAAAkAjhWOV7VNJWSdOMMX3cfmJjJd1vrV2f0ZUB6WGrL5B5fA6BzOIzCGQen0MgszzxGTTWVvd+alWPMaajpPGSDpVz5conJI211gYzuS4AAAAAAADEIhwDAAAAAACAZ7GtEkCEMWaoMeYNY8wKY8xGY8zXxphTM70uwKuMMXu6n0VrjNkt0+sBvMAYk2WMucYY85MxZqsx5ndjzAOZXhfgJcaYU4wx/3X/DlxhjHnGGLNHptcF7IqMMW2MMY8ZY743xgSNMXMTjDHGmOuMMb8ZY4qMMR8ZY7rs/NXuOIRjAKJdKWmjpCskDZb0gaQpxphLMroqwLvulfOZBLDzPC3pUkn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      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bptk.plot_scenarios(\n",
    "    scenarios=[\"base\",\"scenario07\"],\n",
    "    scenario_managers=\"smPopulation\",\n",
    "    equations=[\"population\"],\n",
    "    series_names={}\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to the stock and flow diagram `foodAvailable` influences `foodAvailablePerPerson`. The lesser food we have, the lesser food one person has. `foodAvailablePerPerson` then affects the births and deaths. Lesser people are born and more people die because we don't have enough food for each person. As a result, the population of `scenario07` increases slower than `base`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Export data as \"DataFrame\"\n",
    "\n",
    "We built BPTK-Py with integration in mind. This means, you can easily export the simulation results as so-called \"DataFrames\". This is a standard Python exchange format for data. This means you can easily process the simulation results in other data analysis / data science packages for further processing (Machine Learning, Data enrichment and many more). Just add the argument ``return_df=True`` to the plot_scenarios call:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>smPopulation_base_population</th>\n",
       "      <th>smPopulation_scenario07_population</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>t</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>80000000.0</td>\n",
       "      <td>80000000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.0</th>\n",
       "      <td>80800000.0</td>\n",
       "      <td>80007000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.0</th>\n",
       "      <td>81600000.0</td>\n",
       "      <td>80014000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4.0</th>\n",
       "      <td>82400000.0</td>\n",
       "      <td>80021000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5.0</th>\n",
       "      <td>83200000.0</td>\n",
       "      <td>80028000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6.0</th>\n",
       "      <td>84000000.0</td>\n",
       "      <td>80035000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7.0</th>\n",
       "      <td>84800000.0</td>\n",
       "      <td>80042000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8.0</th>\n",
       "      <td>85600000.0</td>\n",
       "      <td>80049000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.0</th>\n",
       "      <td>86400000.0</td>\n",
       "      <td>80056000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10.0</th>\n",
       "      <td>87200000.0</td>\n",
       "      <td>80063000.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      smPopulation_base_population  smPopulation_scenario07_population\n",
       "t                                                                     \n",
       "1.0                     80000000.0                          80000000.0\n",
       "2.0                     80800000.0                          80007000.0\n",
       "3.0                     81600000.0                          80014000.0\n",
       "4.0                     82400000.0                          80021000.0\n",
       "5.0                     83200000.0                          80028000.0\n",
       "6.0                     84000000.0                          80035000.0\n",
       "7.0                     84800000.0                          80042000.0\n",
       "8.0                     85600000.0                          80049000.0\n",
       "9.0                     86400000.0                          80056000.0\n",
       "10.0                    87200000.0                          80063000.0"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bptk.plot_scenarios(\n",
    "    scenarios=[\"base\",\"scenario07\"],\n",
    "    scenario_managers=\"smPopulation\",\n",
    "    equations=[\"population\"], \n",
    "    series_names={},\n",
    "    return_df=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thanks for working through this tutorial!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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